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Visual Group Theory

Visual Group Theory

£52.00

Part of MAA Problem Book Series

  • Date Published: April 2009
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • format: Hardback
  • isbn: 9780883857571

£ 52.00
Hardback

This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
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About the Authors
  • This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups and understand their significance. It brings groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. Opening chapters anchor the reader's intuitions with puzzles and symmetrical objects, defining groups as collections of actions. This approach gives early access to Cayley diagrams, the visualization technique central to the book, due to its unique ability to make group structure visually evident. This book is ideal as a supplement for a first course in group theory or alternatively as recreational reading.

    • Includes over 300 full-colour illustrations
    • Moves from the basics of group theory to Sylow theory and Galois theory
    • An applications chapter shows how group theory describes the symmetry in crystals, dancing, art, architecture, and more
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    Product details

    • Date Published: April 2009
    • format: Hardback
    • isbn: 9780883857571
    • length: 306 pages
    • dimensions: 262 x 182 x 24 mm
    • weight: 0.8kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
  • Table of Contents

    Preface
    Overview
    1. What is a group?
    2. What do groups look like?
    3. Why study groups?
    4. Algebra at last
    5. Five families
    6. Subgroups
    7. Products and quotients
    8. The power of homomorphisms
    9. Sylow Theory
    10. Galois theory.

  • Author

    Nathan Carter, Bentley College, Massachusetts
    Nathan Carter earned his PhD in mathematics at Indiana University in July 2004. He received the University of Scranton Excellence in Mathematics Award in 1999, an Indiana University Rothrock Teaching Award in 2003, and a Bentley College Innovation in Teaching Award in 2007. Visual Group Theory is his first book, based on lessons learned while writing the software Group Explorer. Like several of his research projects, it puts computers to work to improve mathematical understanding and education.

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